O‘zbekiston respublikasi oliy va o‘rta maxsus ta’lim vazirligi samarqand iqtisodiyot va servis instituti «oliy matematika» kafedrasi
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oliy matematika
Differensial hisob 199. ) (x f y egri chiziqqa ) , ( 0 0 0 y x M nuqtadan o’tkazilgan urinma tenglamasi toping. A) ) )( ( 0 0 0 x x x f y y ) ) )( ( 0 0 0 x x x f y y D) ) )( ( 0 0 0 x x x f y y E) ) 0 ) ( ( ), ( ) ( 1 0 0 0 0 x f x x x f y y 200. ) (x f y egri chiziqqa ) , ( 0 0 0 y x M nuqtadan o’tkazilgan normal tenglamasi toping. A) ) 0 ) ( ( ), ( ) ( 1 0 0 0 0 x f x x x f y y ) ) )( ( 0 0 0 x x x f y y D) ) )( ( 0 0 0 x x x f y y E) ) )( ( 0 0 0 x x x f y y 122 201. 4 3 3 x y egri chiziqqa abssissasi 2 0 x nuqtada o’tkazilgan urinma tenglamasini toping. A) 0 4 3 12 y x ) 0 86 12 3 y x D) 0 4 3 12 y x E) 0 4 3 12 y x 202. 4 3 3 x y egri chiziqqa abssissasi 2 0 x nuqtada o’tkazilgan normalning tenglamasini toping. A) 0 86 12 3 y x ) 0 4 3 12 y x D) 0 86 12 3 y x E) 0 4 3 12 y x 203. Quyidagi differensiallash qoidalaridan qaysilari to’g’ri berilgan: 1) v u v u ) ( ; 2) v u v u v u ) ( ; 3) u c cu) ( ; 4) 2 v v u v u v u . A)1),2),3) ) 1),2),4) D) 2),3),4) E) hammasi 204. Quyidagi differensiallash qoidalaridan qaysilari to’g’ri berilgan: 1) v u v u ) ( ; 2) v u v u v u ) ( ; 3) u c cu) ( ; 4) 2 v v u v u v u . A)1),3),4) ) 1),2),4) D) 2),3),4) E) hammasi 205. Quyidagi differensiallash formulalaridan qaysilari to’g’ri berilgan:1) 0 , ) ( 1 u R n u nu u n n ; 2) ; ) ( u a a u u 3) ; ) ( u e e u u 4) u na u u a 1 1 ) (log . A) 1),3),4) ) 2),3),4) D) 1),2),3) E) hammasi 206. Quyidagi differensiallash formulalaridan qaysilari to’g’ri berilgan: 1) u u u 1 ) (ln ; 2) u u u cos sin ; 3) u u u sin ) (cos ; 4) u u u tg 2 cos 1 ) ( . A) 1),2),4) ) 1),2),3) D) hammasi E) 2),3)4) 207. Quyidagi differensiallash formulalaridan qaysilari to’g’ri berilgan:1) u u u ctg 2 sin 1 ) ( ;2) u u u 2 1 1 ) (arcsin ; 3) u u u 2 1 1 ) (arccos ; 4) u u u arctg 2 1 1 ) ( . 123 A) 1),3),4) ) 1),2),3) D) 2),3),4) E) hammasi 208. Quyidagi differensiallash formulalaridan qaysilari to’g’ri berilgan: 1) u u u arcctg 2 1 1 ) ( ; 2) v nu u u vu u v v v 1 ) ( ; 3) u u u 2 1 1 ) (arccos ; 4) u u u arctg 2 1 1 ) ( . A) 1),2),3) ) 1),2),4) D) hammasi E) 2),3),4) 209. f 2 2 3 ) ( 2 3 funksiya hosilasining x =1 nuqtadagi qiymatini toping. A) 1 f = -11 ) 1 f =15 D) 1 f =13 E) 1 f =11 210. u y sin murakkab funksiyaning hosilasini toping. A) u u y cos ) B u u y sin D) u u y cos E) u u y sin 211. u y arcsin teskari trigonometrik murakkab funksiyasining hosilasini toping. A) 2 1 u u ) 2 1 u u D) 2 1 u u E) 2 1 u 212. x y 7 sin funksiyaning uchinchi tartibli hosilasini toping. A) y 343 x 7 cos ) y =49 x 7 cos D) x y 7 sin 49 E) y =343 x 7 cos 213. x x y sin funksiya hosilasini toping. A) x x x x y 2 sin / cos sin ) x x x x y sin / cos sin D) x x x x y sin / cos sin E) x x x x y 2 sin / cos sin 214. x x y arcsin 2 funksiya hosilasini toping. A) 2 2 1 1 sin 2 x ) x x y arcsin 2 D) x x x x y arccos arcsin 2 2 E) x x x x y arccos arcsin 2 2 215. 2 sin funksiyaning hosilasini toping. A) 2 sin sin 2 ) s 2 D) s 2 2 E) sin 2 216. 2 2 ) 1 ( funksiyaning differensialini toping. A) dx ) 1 ( 4 2 ) ) 1 ( 4 2 D) 2 2 ) 1 ( 4 E) ) 1 ( 2 2 124 217. Hosilaning tarifini toping. A) funksiya orttirmasining argument orttirmasiga nisbati, argument orttirmasi no’lga intilgandagi limitiga aytiladi va quyidagicha belgilanadi: y x y x lim 0 ) / D) x y / E) y x y x lim 0 218. 1 lim 1 x n nx x limitni Lopital qoidasidan foydalanib hisoblang. A) 0 ) 2 D) -1 E) 1 219. 5 45 , 243 ni funksiya differensialidan foydalanib, taqribiy hisoblang. A) 2,8 ) 5,3 D) 3,001 E) 4,2 220. Skalyar maydonga misollar toping. A) temperaturalar maydoni, bosimlar maydoni, zichliklar maydoni ) kuchlar maydoni, tezliklar maydoni D) tezlanishlar maydoni E) faqat kuchlar maydoni 221. 3 2 ) 7 2 ( x y funksiyaning ikkinchi tartibli hosilasini toping. A) ) 7 10 )( 7 2 ( 12 2 2 x x y ) 2 2 ) 7 2 ( 12 x x y D) ) 7 10 )( 7 2 ( 12 2 2 x x y E) ) 7 10 )( 7 2 ( 12 2 2 x x y 222. 100 2 2 y x oshkormas ko’rinishda berilgan, funksiyaning ikkinchi tartibli hosilani toping. A) 3 100 y y ) 3 2 2 y y x y D) 3 100 y y E) y x y / 223. Funksiya orttirmasi uchun formulani toping. A) x x y y ) x x y y D) 2 x x y y E) x x y y 2 224. x f y funksiyaning differensialini toping. A) dx y dy ) x x y dy D) 2 x x y dy E) dy y dx 225. x f y funksiyaning 2-tartibli differensialini toping. A) 2 2 ) ( ) ( dx y dx y d dy d y d ) 2 2 dx y y d D) dx y y d 2 E) dx y y d 2 226. 2 1 x y funksiyaning birinchi tartibli differensialini toping. 125 A) dx x x dy 2 1 ) dx x x dy 2 1 2 D) dx x x dy 2 1 E) dx x dy 2 1 1 227. 2 1 x y funksiyaning ikkinchi tartibli differensialini toping. A) 2 3 2 2 ) 1 ( 1 dx x y d ) 2 3 2 2 2 ) 1 ( 2 dx x y d D) 2 3 2 2 2 ) 1 ( 2 1 dx x y d E) 2 3 2 2 ) 1 ( 1 dx x y d 228. Roll teoremasining shartlari quyidagilarning qaysilarida to’g’ri berilgan: 1) ) (x f funksiya b a, kesmada aniqlangan va uzluksiz; 2) aqalli b a, oraliqda ) (x f chekli hosila mavjud emas; 3) oraliqning chetki nuqtalarida funksiya teng ) ( ) ( b f a f qiymatlarni qabul qiladi A) 1),3) ) 1),2) D) hammasi E) 2),3) 229. Lagranj teoremasining shartlari quyidagilarning qaysilarida to’g’ri berilgan: 1) ) (x f funksiya b a, kesmada aniqlangan va uzluksiz; 2) aqalli b a, ochiq oraliqda chekli ) (x f hosila mavjud; 3) oraliqning chetki nuqtalarida funksiya teng ) ( ) ( b f a f qiymatlarni qabul qiladi A) 1),2) ` )1),3) D) hammasi E) 2),3) 230. Lagranj formulasini toping. A) ) ( ) ( ) ( ) ( a b c f a f b f ) ) ( ) ( ) ( ) ( a b c f a f b f D) ) ( ) ( ) ( ) ( a b c f a f b f E) ) ( ) ( ) ( ) ( a b c f a f b f 231. Teylor formulasini toping. A) 1 1 2 ) ( )! 1 ( ) ( ! ) ( .... ) ( ! 2 ) ( ) ( ! 1 ) ( ) ( ) ( n n n n a x n a x a f a x n a f a x a f a x a f a f x f ) 1 1 2 ) ( )! 1 ( ) ( ! ) 0 ( .... ) ( ! 2 ) 0 ( ) ( ! 1 ) 0 ( ) 0 ( ) ( n n n n a x n x f a x n f a x f a x f f x f 126 D) 1 1 2 )! 1 ( ) ( ! ) ( .... ! 2 ) ( ! 1 ) ( ) ( ) ( n n n n x n a x a f n a f x a f x a f a f x f E) 1 1 2 ) ( )! 1 ( ) ( ! ) ( .... ) ( ! 2 ) ( ) ( ! 1 ) ( ) ( ) ( n n n n a x n a x a f a x n a f a x a f a x a f a f x f 232. Makloren formulasini toping. A) 1 1 2 )! 1 ( ) ( ! ) 0 ( ... ! 2 ) 0 ( ! 1 ) 0 ( ) 0 ( ) ( n n n n x n x f x n f x f x f f x f ) 1 1 2 )! 1 ( ) ( ! ) ( ... ! 2 ) ( ! 1 ) ( ) ( ) ( n n n n x n x f x n a f x a f x a f a f x f D) 1 1 2 )! 1 ( ) ( ! ) 0 ( ... ! 2 ) 0 ( ! 1 ) 0 ( ) 0 ( ) ( n n n n x n x f x n f x f x f f x f E) 1 1 2 ) 1 ( ) ( ) 0 ( ... 2 ) 0 ( 1 ) 0 ( ) 0 ( ) ( n n n n x n x f x n f x f x f f x f 233. Monotonlikning zaruriy va yetarli shartlari quyidagilarning qaysilarida to’g’ri berilgan: 1) ) , ( b a oraliqda differensiallanuvchi, ) (x f y funksiya musbat hosilaga ega, ya’ni , 0 ) (x f bo’lsa, funksiya shu oraliqda o’suvchi bo’ladi; 2) ) , ( b a oraliqda differensiallanuvchi ) (x f y funksiya musbat hosilaga ega, ya’ni , 0 ) (x f bo’lsa, funksiya shu oraliqda kamayuvchi bo’ladi; 3) ) , ( b a oraliqda differensiallanuvchi ) (x f y funksiya manfiy hosilaga ega, ya’ni , 0 ) (x f bo’lsa, funksiya shu oraliqda kamayuvchi bo’ladi. A) 1),3) ) 2),3) D) hammasi E) 1),2) 234. 4 6 2 3 ) ( 2 3 x x x x f y funksiyaning monotonlik oraliqlarini toping. A) ) ; 2 ( , ) 2 ; 1 ( , ) 1 ; ( ) ) 1 ; ( , ) ; 2 ( D) ) 1 ; ( , ) 2 ; 1 ( E) ) 2 ; 1 ( , ) ; 2 ( 235. Funksiyaning ekstremumi ta’riflari quyidagilarning qaysilarida to’g’ri berilgan: 1) 0 x nuqtaning shunday atrofi mavjud bo’lsaki, bu atrofning har qanday 0 x x nuqtasi uchun ) ( ) ( 0 x f x f tengsizlik bajarilsa, ) (x f y funksiya 0 x nuqtada maksimumga ega deyiladi; 2) 0 x nuqtaning shunday atrofi mavjud bo’lsaki, bu atrofning har qanday 0 x x nuqtasi uchun ) ( ) ( 0 x f x f tengsizlik 127 bajarilsa, ) (x f y funksiya 0 x nuqtada maksimumga ega deyiladi; 3) 0 x nuqtaning shunday atrofi mavjud bo’lsaki, bu atrofning har qanday 0 x x nuqtasi uchun ) ( ) ( 0 x f x f tengsizlik bajarilsa, ) (x f y funksiya 0 x nuqtada Download 1.79 Mb. Do'stlaringiz bilan baham: |
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